利用等价无穷小求函数极限

Application of Equivalent Infinitesimal in Function Limit

摘要: 在求解函数极限的过程中，选择正确的方法可以事半功倍，避免计算过程的繁琐，而利用等价无穷小是一种具有代表性的途径，具有快速、简便、适用性强等优点。因此，有必要探讨如何在函数极限中运用等价无穷小从而简化运算。本文主要基于函数极限知识和常用的等价无穷小，对等价无穷小的比较、代换定理及等价关系进行介绍，探究其在不同函数极限中的应用，并且辅以例题举证。

Abstract: In the process of solving the function limit, the method of selecting pairs can get twice the result with half the effort, avoiding the complicated calculation process. Equivalence infinitesimal is a kind of representative algorithm with its advantages of quickness, simplicity and strong applicability. It can be used to solve the limit problems that are difficult to be solved by other methods, so as to simplify the complexity and make the difficulty easy. The basic method is to replace some infini-tesimal factors with its equivalent infinitesimal in the process of finding the limit, so as to achieve the purpose of simplifying the operation. Therefore, it is necessary to explore the application of equivalent infinitesimal in finding function limit. Based on the knowledge of function limit and equivalent infinitesimal in common use, this paper introduces the comparison of equivalent infini-tesimal, substitution theorem and equivalent relation, explores its application in different function limit, and verifies it with examples.